The area of the two triangles are and
Further explanation:
The areas of two similar triangles are proportional to the squares of their perimeters.
Given:
The sum of areas of triangle is
The ratio of the perimeters of two similar triangles is
Explanation:
Consider the area of first triangle as X.
Consider the area of second triangle as Y.
The ratio of the perimeter of the triangle is 4:7.
The ratio of the areas of the triangles can be obtained as follows,
The sum of areas of triangle is
Substitute for in equation
The area of first triangle can be obtained as follows,
The area of the two triangles are and
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Triangles
Keywords: Ratio, perimeter, similar, similarity, triangles, proportional, square, area, area of triangle, two similar triangles, sum, sum of areas, 65 cm2, 4:7, corresponding sides.